Captain Birdseye,

Indeed, where a performance has been recorded then the performer has copyright in that performance, and also where there is any element of arrangement. In those circumstances a collector certainly has an ethical (and possibly legal) responsibility to respect that, and not for example to induce the performer to sign away his rights on terms which are not equitable.

But where a performer is simply a custodian (perhaps one of many) of a traditional piece, who happens to be the one from whom it is collected, it is difficult to argue that they have any particular rights over the song or tune itself.

Whenever you or I perform a traditional piece, it is thrown out there for anybody to pick up. If they substantially copy your arrangement then they are breaching your copyright in that, but if they make their own arrangement you have no right to prevent them performing, recording or publishing it, any more than the source from whom you got it can stop you.